# Learning equilibria with personalized incentives in a class of nonmonotone games

arXiv: https://arxiv.org/abs/2111.03854 · HTML: https://mlsanity.com/paper/2111.03854/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 34 references that are in the map.
- First posted on arXiv 6 Nov 2021.

## Builds on (most cited first, 11 of 11)

- [How to Escape Saddle Points Efficiently](https://mlsanity.com/paper/1703.00887/) (2017)
- [Stochastic model-based minimization of weakly convex functions](https://mlsanity.com/paper/1803.06523/) (2018)
- [Online Learning with Inexact Proximal Online Gradient Descent Algorithms](https://mlsanity.com/paper/1806.00202/) (2018)
- [Distributed Nash Equilibrium Seeking by A Consensus Based Approach](https://mlsanity.com/paper/1602.00771/) (2016)
- [Distributed Personalized Gradient Tracking with Convex Parametric Models](https://mlsanity.com/paper/2008.04363/) (2020)
- [Personalized Optimization with User's Feedback](https://mlsanity.com/paper/1905.00775/) (2019)
- [Charging plug-in electric vehicles as a mixed-integer aggregative game](https://mlsanity.com/paper/1910.10272/) (2019)
- [Solving non-monotone equilibrium problems via a DIRECT-type approach](https://mlsanity.com/paper/2002.12198/) (2020)
- [Personalized Demand Response via Shape-Constrained Online Learning](https://mlsanity.com/paper/2006.06932/) (2020)
- [On the exact convergence to Nash equilibrium in hypomonotone regimes under full and partial-information](https://mlsanity.com/paper/2104.11096/) (2021)
- [Nash equilibrium seeking in potential games with double-integrator agents](https://mlsanity.com/paper/1811.07569/) (2018)

## Built on by (most cited first, 2 of 2)

- [Personalized incentives as feedback design in generalized Nash equilibrium problems](https://mlsanity.com/paper/2203.12948/) (2022)
- [An active learning method for solving competitive multi-agent decision-making and control problems](https://mlsanity.com/paper/2212.12561/) (2022)

## Abstract (arXiv)

We consider quadratic, nonmonotone generalized Nash equilibrium problems with symmetric interactions among the agents. Albeit this class of games is known to admit a potential function, its formal expression can be unavailable in several real-world applications. For this reason, we propose a two-layer Nash equilibrium seeking scheme in which a central coordinator exploits noisy feedback from the agents to design personalized incentives for them. By making use of those incentives, the agents compute a solution to an extended game, and then return feedback measures to the coordinator. We show that our algorithm returns an equilibrium if the coordinator is endowed with standard learning policies, and corroborate our results on a numerical instance of a hypomonotone game.